This chapter introduces a bounded model predictive control (BMPC) framework tailored for the attitude and vibration control (AVC) of rigid-flexible coupling (RFC) satellites subject to multi-source uncertainties. Addressing the complexity of high-dimensional satellite systems, the chapter begins by establishing a nominal RFC dynamic model and proposing an interval uncertainty-based discretization method to process unknown-but-bounded (UBB) system parameters. A novel BMPC strategy is then developed, rooted in the interval dimension-wise analysis (IDWA) technique, to efficiently predict the bounds of control inputs, attitude angles, and flexible deflections. To further ensure operational safety, interval-based time-dependent reliability (ITDR) assessment is integrated into the control framework, evaluating system performance under various operational situations. Numerical validations confirm that this interval-based approach achieves approximation accuracy comparable to Monte Carlo simulations (MCSs) but with significantly reduced computational time, establishing a solid foundation for real-time control of uncertain satellite systems.